High density electrode arrays form the backbone of many molecular sensing applications (e.g., high density electrode micro-arrays in deoxyribonucleic acid (DNA) hybridization, protein detection, etc.), and can include a platform in which a large number (e.g., several hundred/thousands) of multiplexed electrode channels are provided, which are capable of parallel operation. In the course of an experiment, a number of electrodes in a high density array can exhibit outlier behavior, which refers to any behavior that causes the current-voltage (I-V) characteristic of an electrode to significantly deviate from that of most others of the electrodes. Generally, the I-V characteristics of most of the electrodes reside within a predefined acceptable range, and an electrode is considered to significantly deviate from that of the general population of electrodes if the I-V characteristics of the electrode are more than three standard deviations from the mean of the I-V characteristics of the general population of electrodes. Similarly, an electrode can also be considered to significantly deviate if the I-V characteristics of the electrode exceed a user-defined threshold.
Such outlier behavior can be caused many factors. For example, with regard to Indium-Tin-Oxide (ITO) electrodes formed on a glass substrate, outlier behavior may be the result of tin variations causing formation of unstable hydrogel on the surface of the electrode. Generally, the surface of the ITO electrode is composed of different species with dynamically varying concentrations, which are responsible for electrochemical “hot-spots” (e.g., a lot of activity) and “dead-zones” (e.g., very little or no activity). The outlier behavior can also be dynamic in nature, where an electrode exhibits outlier behavior for some portion of the experiment and functions normally during another portion of the experiment.
Methods to determine outlier behavior in electrodes include either (1) periodically testing each electrode on an individual basis during the course of an experiment or (2) re-validating any data points that significantly deviated from expected values to rule out outlier behavior as the cause of the deviation.
Generally, the first option is useful for (a) low density electrode arrays (i.e., an array with a small number of electrodes) or (b) high density electrode arrays with a single faulty electrode. With regard to low density electrode arrays, assuming that a typical electrochemical measurement takes about six seconds, each electrode of the array can be tested on an individual basis (i.e., encompassing one measurement) in a relatively short period of time. In other words, during each measurement, a voltage is applied to a single electrode and the current drawn from that electrode is compared to an expected value to determine if it is an outlier. To detect a single faulty electrode among an electrode array with ‘N’ electrodes of a high density electrode array, log2N measurements would need to be performed. In other words, for the first measurement, a voltage is applied to two subsets (with each subset containing N/2 electrodes) of the N electrodes and the linear sums of the currents drawn from each of the subsets are compared to an expected current value for each of the subsets. Therefore, if a current sum of one of the subsets deviates from an expected current value, then it can be assumed that the subset contains the outlier. Thus, in order to determine which electrode is the outlier, the above process (i.e., splitting the array of electrodes into two equal subsets during the measurement) is repeated for each subset indicated as including an outlier in a prior iteration. For example, to detect one electrode among a 4096-element array, it would take log2(4096) or 12 measurements. Therefore, assuming that each measurement takes six seconds to perform, determining the single outlier among the 4096 element array would take around 72 seconds.
However, as the number of outlier electrodes increase, the number of measurements required to identify them (i.e., with a high level of confidence) approaches the total number of electrodes. In general, in order to determine more than 1 outlier in an N element array, the number of required measurements rapidly approaches N, requiring almost all of the electrodes to be individually monitored. This is because outlier behavior occurs in both the positive and negative direction and, therefore, merely summing the currents of a subset of electrodes may not show any significant deviation from an expected current value for the subset. Accordingly, applying the log2N approach would prove futile. Therefore, to determine more than 1 outlier in a 4096-element array, it would take nearly 4096 measurements, which translates to nearly seven hours of measurement time (assuming that each measurement takes six seconds to perform). Moreover, the above-mentioned outlier monitoring may need to be performed several times during the course of an experiment due to the dynamic nature of the underlying phenomena.
Further, the second option (i.e., re-validating any data points that significantly deviate from expected values to rule out outlier behavior as the cause of the deviation) is not very attractive because, in many cases, it would require the repetition of an entire experiment, which might not be practical due to a variety of reasons including, but not limited to, additional cost, limited quantity of samples.